Can't get 'true white' video output
Your render inside Blender is not pure white.

After rendering clic on the white part of your render in the UV/imge editor, watch the values in the bottom part, R 0.92, G 0.92, B 0.92.

You just need pure texture color and lighting, it's too hazardous to try setting the right orientation and strength of a sun to have perfect texture color. You lose some light during ray casting.

You want two things to compose in post processing:


the animation of the logo and the text with the correct RGB values (no need of light for that).
the shadows themselves (need light or tricks that I don't know).


Make a scene without light, and replace the diffuse shaders by emission ones. Now you have the real textures colors, same for the white background. Bonus: you can set the samples to 10 or 20 it's enough

Make a second scene with only the sun, the white background and the text for the shadows. Background and text must have diffuse shader this time. On the render layer panel, under passes activate shadow. Render the frames that matter for the Shadows.

Plug the shadow passe in the fac of a color mix node, put the animation of the logo and text in the second image slot of the mix node, the first one is the color of your shadows.